In engines of such type as rotary engines or two cycle reciprocating engines, it is known that they tend to repeat at random the ignition and the failure of ignition, which causes variation in torque and generation of disagreeable noise from the engines. Of late, there has been proposed an ignition system for an internal combustion engine which is so designed that the failure of ignition and the ignition are periodically repeated when the engine is decelerated or idling so as to prevent such variation in torque and disagreeable noise. Conventionally, such type ignition system has two sets of ignition circuits each including an ignition coil the primary coil element of which is connected to a contact breaker. One of the ignition circuits has the operative frequency of the corresponding contact breaker set at one half of that of the contact breaker in the other ignition circuit. In normal operation of the engine, the other ignition circuit operates, but when the engine is decelerated or idling, the one ignition circuit operates so that the engine ignites with one half of the frequency on normal operation of the engine. However, such type system makes maintenance and inspection troublesome because of two contact breakers provided therein. Furthermore, a mechanical reduction mechanism is required for reducing the operating frequency of the contact breaker in the first ignition circuit, which causes complicated construction of the ignition system and as a result such type system cannot be easily installed in the conventional engine.